We study the homomorphism problem for infinite relational structures which can be defined by finitely many first-order formulas over the natural numbers with equality. We determine the decidability status of this problem depending on whether the signature or/and the number of tuples in a single relation are allowed to be infinite.

Joint work with Bartek Klin, Eryk Kopczyński, Sławek Lasota and Szymon Toruńczyk.

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